Math Problem Statement

A number, x, rounded to 2 decimal places is 15.31. Write down the error interval for x.

Solution

To find the error interval for xx when xx is rounded to two decimal places as 15.3115.31, we should consider the range of values that could round to 15.3115.31.

Solution:

  1. Identify the rounding rule: Since xx is rounded to two decimal places, any number in the range from 15.30515.305 to 15.31515.315 will round to 15.3115.31.

  2. Define the interval:

    • The lower bound (inclusive) is 15.30515.305.
    • The upper bound (exclusive) is 15.31515.315.

Final Answer:

The error interval for xx is: 15.305x<15.31515.305 \leq x < 15.315

Would you like more details on how to find error intervals?

Here are five related questions for further exploration:

  1. What is the error interval for a number rounded to one decimal place, for example, 8.48.4?
  2. How would the error interval change if xx was rounded to three decimal places instead of two?
  3. Can you explain how to determine error intervals for different rounding methods, such as rounding up or down?
  4. How does an error interval differ from a confidence interval in statistics?
  5. What are some practical applications of error intervals in measurement and science?

Tip: Remember that error intervals represent all possible values a rounded number could have been before rounding. This helps ensure accuracy in scientific measurements and calculations.

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Math Problem Analysis

Mathematical Concepts

Rounding
Error Interval

Formulas

Error interval for rounding to n decimal places

Theorems

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Suitable Grade Level

Grades 7-9